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Is there an application which can calculate an area of any two-dimensional figure limited by some function graphs? I would like to know so I can have some method of confirming my calculations. There are some applications but they offer a limited number of shapes.

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It is the point of the integral. If your area is limited by the graph of a function $f$, then the area under $f$ (if $f$ is positive) is:

$$\int_{[a,b]\times [c,d]} f(x,y)\mathrm{d}(x,y).$$

Edit.

If you really want a function like you stated in the comments, you can consider:

$$\Phi_{a,b,c,d} \ f\colon \mapsto \int_{[a,b]\times [c,d]} f(x,y)\mathrm{d}(x,y).$$

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    Yes, but i want to know is there some application which enables you to enter some functions and get area that is limited by them. Just to check my results. – 2017-02-10